Brian Miller posts a smorgasbord of applied proportions activities, each of which poses students as crime scene investigators. He also gives purpose to the skills he wants to teach by fitting them inside a larger, more enticing question:
The basic premise is as follows: I show the Bone Collector clip first. I tell them we need to figure out the shoe size of the killer because we need to make sure that the killer is not in the room. Then I concede that I realize they are not trained investigators. Thus I tell them that over the next couple days we will be doing some investigator training, to get them ready to take on this case.
In some recently consulting, I was asked how to make to make trig identities less of a slog. I didn't hesitate to send along Section 2 of Sam Shah's worksheet. Section 2 really needs its own post. Briefly: watch how he sets students up for a major cognitive conflict as they all graph (seemingly) different trig functions only to compare and find out they're exactly the same. "Okay, are you all graphed? On the count of three there will be the big reveal. One … TWO … REVEAL! Whoa. Really? REALLY? Yes, really." (I don't think I've seen anybody else pull off Sam's worksheet persona, which is some kind of cross between "reality TV host" and "Vegas lounge act.") The point of the worksheet isn't practice. It isn't instruction. It collects student hypotheses about a discrepant event which they'll be working on "as we go through the next few days." If math class were a movie, Sam's worksheet would be the trailer.
Julie Reulbach encourages us to "save the math for last" in a very nice modeling activity. But questions like "what do we need here?" are modeling. They are math. Is it more accurate to say, "Save the computation for last?"
Never before had “test points” seemed so obvious to them. Test points were not just random points, they meant something. They told a story. The next day, when we finally got to the actually inequality lesson, foldable, and then homework, the students really understood the need for a test point. They also easily understood the horrific workbook word problem.
Bruce Ferrington asks students "What is my area?":
My chief interest here is to look at how the kids are going to approach this question. I want to see if they can come up with any short-cuts that will speed up the calculations, so they don't have to cover their entire body in 1cm grid paper and count out each square. Look what they did!
2013 Mar 22. Sam Shah wrote up his thinking behind the worksheet.
Maybe, save the “procedures” for last? You know, the actual lesson with the steps and the summary of all of the rules they discovered but didn’t realize it.